As the title says, the game crashes randomly, without even any slowdown. I know my laptop isn't exactly cutting edge since it was only like $330, so I wouldn't be surprised if the response I get is "Give up, your system is too weak to play the game," but I thought I would at least ask so I don't waste my time trying to fix something that can't be fixed.

I'm pretty sure Dolphin under Windows 8 and above has random crashes that no one has yet determined the exact cause. If this has in fact been fixed, you should try the latest development revisions. Even if the issue isn't fixed in the latest dev builds, you should use them since they're a lot faster than 4.0.2.

Just download the latest, extract it (don't try to run Dolphin from the archive itself) and that should set you up. The dev builds don't have an installer, you just run the executable any time you want to try the latest and greatest builds.